It does ... it sets this value in a BASIC variable that is used for all output. Not sure where it is - you can use the monitor and search $100-$3FF for any change after the color command 🙂 Without now really knowing it I expect that the color command exactly creates this color byte and stores it in this variable to be used by any print char command later on to fill it into the screen ram.
The VERA does not know anything about colors in that sense. It has the tilemap information (actually the Screen Ram is a tileset, where each tile contains a monochrome letter and the color byte points to palette entries). So the print char routines are not using any VERA technology. They just write the char to a certain position int screen ram and set the color information for the color byte.
Really recommend you read the very good stuff on 8bitcoding.com ( no it is not from me 😄)